{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "89bc62cb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from friends import retrieve_observable_and_ansatz\n",
    "obsv, qc, params = retrieve_observable_and_ansatz()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ecedcc78",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PauliSumOp(SparsePauliOp(['IIII', 'XXXX', 'YXYX', 'IZXX', 'ZZXX', 'IIXX', 'ZIXX', 'XYXY', 'YYYY', 'IIIZ', 'XXZZ', 'XXIZ', 'IZIZ', 'IZZZ', 'ZZZZ', 'ZZIZ', 'IIZZ', 'ZIZZ', 'ZIIZ', 'XXZI', 'XXII', 'IZII', 'IZZI', 'ZZZI', 'ZZII', 'IIZI', 'ZIZI', 'ZIII'],\n",
       "              coeffs=[-1.40343802e+01+0.j,  1.89666179e-02+0.j, -1.89666179e-02+0.j,\n",
       " -1.89666179e-02+0.j,  1.89666179e-02+0.j,  1.89666179e-02+0.j,\n",
       " -1.89666179e-02+0.j, -1.89666179e-02+0.j,  1.89666179e-02+0.j,\n",
       " -1.60527381e-01+0.j,  5.30165769e-03+0.j,  5.30165769e-03+0.j,\n",
       " -2.41584122e-01+0.j,  8.88184955e-02+0.j,  9.94831530e-02+0.j,\n",
       " -8.88798376e-02+0.j,  8.58722654e-02+0.j,  8.88184955e-02+0.j,\n",
       " -8.88184955e-02+0.j,  5.30165769e-03+0.j,  5.30165769e-03+0.j,\n",
       "  2.41584122e-01+0.j, -8.88184955e-02+0.j, -8.88798376e-02+0.j,\n",
       "  9.94831530e-02+0.j, -1.60527381e-01+0.j, -2.41584122e-01+0.j,\n",
       "  2.41584122e-01+0.j]), coeff=1.0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obsv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f1929ae7",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2294.16x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw('mpl', fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8e3eba2f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.19535462771567846, 12.167984734279953, 0.19535462771567846]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e3834c1c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.primitives import Estimator\n",
    "estimator = Estimator()\n",
    "job = estimator.run(circuits=qc, observables=obsv, parameter_values=params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "16c2e405",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EstimatorResult(values=array([-14.60295835]), metadata=[{}])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e24eaf2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "results = []\n",
    "results.append(job.result().values[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9192b1dd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import Options\n",
    "\n",
    "options = Options()\n",
    "options.optimization_level = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "362b71b6",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService, Session, Estimator\n",
    "\n",
    "service = QiskitRuntimeService()\n",
    "backend = service.get_backend('ibm_lagos')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "52fee343",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "with Session(service=service, backend=backend) as session:\n",
    "    estimator = Estimator(options=options)\n",
    "    job = estimator.run(circuits=qc, observables=obsv, parameter_values=params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "279b27c6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EstimatorResult(values=array([-14.21913395]), metadata=[{'variance': 0.3198837586455653, 'shots': 4000}])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2942e3ef",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "results.append(job.result().values[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "429835b1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "options.optimization_level = 2\n",
    "options.transpilation.layout_method = \"sabre\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "60f72534",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Options(optimization_level=2, resilience_level=None, max_execution_time=None, transpilation=TranspilationOptions(skip_transpilation=False, initial_layout=None, layout_method='sabre', routing_method=None, approximation_degree=None), resilience=ResilienceOptions(noise_amplifier='TwoQubitAmplifier', noise_factors=(1, 3, 5), extrapolator='LinearExtrapolator'), execution=ExecutionOptions(shots=4000, init_qubits=True), environment=EnvironmentOptions(log_level='WARNING', callback=None, job_tags=[]), simulator=SimulatorOptions(noise_model=None, seed_simulator=None, coupling_map=None, basis_gates=None))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cb1e33e3",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "with Session(service=service, backend=backend) as session:\n",
    "    estimator = Estimator(options=options)\n",
    "    job = estimator.run(circuits=qc, observables=obsv, parameter_values=params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e79054ba",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EstimatorResult(values=array([-14.53703338]), metadata=[{'variance': 0.11849432741875174, 'shots': 4000}])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "cd9e3658",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "results.append(job.result().values[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "96c7b63a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "options.optimization_level = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cc63b626",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "options.resilience_level = 1\n",
    "\n",
    "with Session(service=service, backend=backend) as session:\n",
    "    estimator = Estimator(options=options)\n",
    "    job = estimator.run(circuits=qc, observables=obsv, parameter_values=params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7ee6b117",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EstimatorResult(values=array([-14.54698572]), metadata=[{'variance': 0.16701960026941956, 'shots': 4000, 'readout_mitigation_num_twirled_circuits': 16, 'readout_mitigation_shots_calibration': 8192}])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "6839233d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "results.append(job.result().values[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4f10f9fd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "options.resilience_level = 2\n",
    "options.resilience.noise_amplifier = 'TwoQubitAmplifier'\n",
    "options.resilience.noise_factors = (1, 1.2, 1.5)\n",
    "options.resilience.extrapolator = 'LinearExtrapolator'\n",
    "\n",
    "with Session(service=service, backend=backend) as session:\n",
    "    estimator = Estimator(options=options)\n",
    "    job = estimator.run(circuits=qc, observables=obsv, parameter_values=params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "68f1ca01",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EstimatorResult(values=array([-14.59176797]), metadata=[{'zne': {'noise_amplification': {'noise_amplifier': \"<TwoQubitAmplifier:{'noise_factor_relative_tolerance': 0.01, 'random_seed': None, 'sub_folding_option': 'from_first'}>\", 'noise_factors': [1, 1.2, 1.5], 'values': [-14.543479768105339, -14.512218600605587, -14.51305556999569], 'variance': [0.12659279703299403, 0.1419320289939639, 0.1640169091918978], 'shots': [4000, 4000, 4000]}, 'extrapolation': {'extrapolator': 'LinearExtrapolator'}}}])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ec339fef",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "results.append(job.result().values[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "55c21cae",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from datetime import datetime\n",
    "\n",
    "def interim_results_callback(job_id, result):\n",
    "    now = datetime.now()\n",
    "    print(now, \"*** Callback ***\", result, \"\\n\")\n",
    "    \n",
    "options.optimization_level = 0\n",
    "options.execution.shots = 300\n",
    "options.environment.callback = interim_results_callback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "07a00854",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "options.resilience_level = 3\n",
    "\n",
    "with Session(service=service, backend=backend) as session:\n",
    "    estimator = Estimator(options=options)\n",
    "    job = estimator.run(circuits=qc, observables=obsv, parameter_values=params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64504a51",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "```\n",
    "2023-03-16 18:59:00.897374 *** Callback *** {'unique_layers_detected': 3, 'total_layers': 70} \n",
    "\n",
    "2023-03-16 19:01:12.812642 *** Callback *** {'msg': 'Sampling overhead for layer 1/3: 1.0381497062307443'} \n",
    "\n",
    "2023-03-16 19:03:21.394775 *** Callback *** {'msg': 'Sampling overhead for layer 2/3: 1.0418104322947281'} \n",
    "\n",
    "2023-03-16 19:04:45.393501 *** Callback *** {'msg': 'Sampling overhead for layer 3/3: 1.0308667982144537'} \n",
    "\n",
    "2023-03-16 19:04:45.588625 *** Callback *** {'sampling_overhead_by_layer': [1.0308667982144537, 1.0418104322947281, 1.0381497062307443], 'unique_layers': 3, 'total_sampling_overhead': 1.4439176359094685} \n",
    "\n",
    "2023-03-16 19:10:00.282664 *** Callback *** {'values': [-15.004731920399502], 'metadata': [{'standard_error': 0.4063455807551261, 'confidence_interval': [-15.161583714947211, -14.847880125851793], 'confidence_level': 0.95, 'shots': 55424, 'samples': 433, 'sampling_overhead': 1.4439176359094685, 'total_mitigated_layers': 10}]} \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ac4aea23",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EstimatorResult(values=array([-15.00473192]), metadata=[{'standard_error': 0.4063455807551261, 'confidence_interval': [-15.161583714947211, -14.847880125851793], 'confidence_level': 0.95, 'shots': 55424, 'samples': 433, 'sampling_overhead': 1.4439176359094685, 'total_mitigated_layers': 10}])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "db3af8c8",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "results.append(job.result().values[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "e8cf5924",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Energy')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(range(len(results)-1), results[1:], ls= ' ', marker='o')\n",
    "plt.plot([0, len(results)-1], [results[0], results[0]], ls='--')\n",
    "plt.xlabel('Mitigation Strategy')\n",
    "plt.ylabel('Energy')"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "qiskit (stable)",
   "language": "python",
   "name": "qiskit-stable"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  },
  "rise": {
   "theme": "monokai",
   "transition": "none"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
